Ray’s Reflections

on adventures in uncertainty

Analyzing paired data with unknown pairings

Summary of progress towards a better test procedure

Concerns about anonymity in experimental design sometimes preclude the pairing of observations within a pre-versus-post intervention study. Such schemes result in paired data with unknown pairings, an issue for practitioners who wish to test for the difference between pre- and post-intervention means, commonly accomplished with the paired t-test. Reliance on a lower-bound estimate of the sample correlation, such as zero, is sensible when pairings are entirely unknown and positive correlation is suspected; this assumption yields the classic two-sample t-test. However, when limited information is available through partially-known pairings, one can improve statistical power by relaxing the assumption of independence. I demonstrate substantial improvement in power attained through an estimate of the sample correlation using partial information, and provide rationale that a test constructed from this estimate would not yield greater-than-nominal type I error probability.

Cathedrals of Climbing

Analyzing stair-climbing workouts in new mountain athletes

For 30 years, the Explorer’s Club of Pittsburgh has run a mountaineering school through the winter, guiding students in outings and exercises to build advanced skills for mountain climbing. Every student of the mountaineering school trains on the stairs of the University of Pittsburgh’s Cathedral of Learning. A typical training session consists of multiple repetitions up the Cathedral’s 34-story stairwell, carrying a weighted backpack to simulate real mountain ascents. I analyzed data from 10 years of training logs, including 129 students and 10,000+ repetitions of the stairs. From 2011-present, students’ climbing paces exhibited consistent response to heavier packs and footwear.

Simple Board Game Simulation in R

I was at a friend’s house for game night last weekend, and I was introduced to a game called The Mind. The premise is simple; a deck of cards is numbered one through one…

Alpine Climbing in the North Cascades

Over a long weekend in July 2025, six ECP’ers convened for an alpine climbing trip in the Washington Pass area of North Cascades National Park. While other ECP’ers were in…

Rethinking Some Statistical Principles

I’ve begun reading Statistical Rethinking by Richard McElreath,¹ and I wanted to log some of my thoughts that come to mind while working through his ideas on modern…

A Tool to Visualize Outdoor Climbing Performance

Recently, I’ve been interested in developing ways to assess my own performance as an outdoor rock climber. One classic tool for evaluating a climber’s history on routes is…

A Summary of My Research in Stats and Medicine

In this post, I review progress in my research so far, and distill my work into three themes spanning topics in biomedical sciences and applied statistics.

Alpine Training in West Virginia’s Wilderness

In one of my first Winter Mountaineering outings with the Explorer’s Club of Pittsbugh (ECP), we hiked through the night to simulate an alpine rock climbing objective–only…

Climbing the Sharkstooth of Rocky Mountain

On July 17, 2022, on a clear day in Rocky Mountain National Park, Jason and I succesfully climbed the Northeast Ridge of Sharkstooth (5.6, II). The spire stands tall behind…

Summiting the Grand Teton via Exum Ridge

My first real mountaineering trip, climbed overnight between August 12-13, 2021. Donnie and I I summitted the Grand Teton using a classic rock climbing route (Exum Ridge…